The solvability of a kind of generalized Riemann–Hilbert problems on function spaces \(H_{\ast }\)

Journal of inequalities and applications

article

Pingrun Li¹ 

[1] School of Mathematical Sciences, Qufu Normal University

关键词: Riemann–Hilbert problems;    Singular integral equations;    Sokhotski–Plemelj formula;    Canonical function;    Function spaces \(H_{\ast }\);   

DOI  :  10.1186/s13660-020-02501-x

学科分类：电力

来源: SpringerOpen

【 摘 要 】

In this paper, we study a kind of generalized Riemann–Hilbert problems (R-HPs) with several unknown functions in strip domains. We mainly discuss methods of solving R-HPs with two unknown functions and obtain general solutions and conditions of solvability on function spaces $H_{\ast }$ . At the end of this paper, we consider in detail the behavior of the solution at ∞ and in different domains. Thus the results in this paper generalize and improve the theory of the classical Riemann–Hilbert problems.

【 授权许可】

CC BY